Chain Description

Protein/Subunit(s) Active Form Serum Cone. (mg/L) Weight (chains) Description and Role of the Active Form in These Pathways... 

This example of a flexible polymer chain in the presence of an external field serves to demonstrate how the use of the limit of a continuous chain leads to distributions that satisfy differential equations. This limit therefore introduces an analogy between the configurations of the continuous equivalent chain and the path of a particle which is undergoing Brownian or diffusive motion. - It is also useful to relate this continuous chain description to Feynman s path integral formulation of quantum me-chanics. This relationship permits the exploitation of mathematical analogies which might lead to suitable approximation schemes. Reference is made to the book by Feynman and Hibbs for certain mathematical details which can be transcribed between quantum mechanical and polymer problems. 

This brings us to the conclusion that as far as the depletion interaction is concerned ideal polymer chains to a good approximation can be replaced by penetrable hard spheres with a diameter a = 2, where the depletion thickness bs now depends on the size ratio q = Rg/R. In dilute polymer solutions the ideal chain description suffices to describe depletion effects. In Chap. 4 we shall see that for polymers with excluded volume the depletion thickness not only depends on the size ration q but also on the polymer concentration, see also [36, 39-41]. Also the (osmotic) pressure is no longer given by the ideal (Van t Hoff) expression. Both features significantly affect depletion effects. 

Three chains and eight chains description for the estimate of the back stress tensor b... 

Different from the ideal chain description, the persistent chain model is not only able to deal with short chains, but also addresses the effect of temperature. Another model, which will introduced as the Ising chain in the next section, accomplishes these tasks in an even more detailed, rather perfect manner. 

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